GTNYieldFunction

Source: models/solid_mechanics/plasticity/GTNYieldFunction.py

Gurson-Tvergaard-Needleman yield function for poroplasticity. The yield function is defined as \(f = \left( \frac{\bar{\sigma}}{\sigma_y + k} \right)^2 + 2 q_1 \phi \cosh \left( \frac{1}{2} q_2 \frac{3\sigma_h-\sigma_s}{\sigma_y + k} \right) - \left( q_3 \phi^2 + 1 \right)\), where \(\bar{\sigma}\) is the von Mises stress, \(\sigma_y\) is the yield stress, \(k\) is isotropic hardening, \(\phi\) is the porosity, \(\sigma_h\) is the hydrostatic stress, and \(\sigma_s\) is the void growth back stress (sintering stress). \(q_1\), \(q_2\), and \(q_3\) are parameters controlling the yield mechanisms.

Inputs

flow_invariant — input · Scalar · required

Effective stress driving plastic flow

poro_invariant — input · Scalar · required

Effective stress driving porous flow

void_fraction — input · Scalar · required

Void fraction (porosity)

isotropic_hardening — input · Scalar

Isotropic hardening

Outputs

yield_function — output · Scalar · required

Yield function

Parameters

yield_stress — parameter · Scalar · required

Yield stress

q1 — parameter · Scalar · required

Parameter controlling the balance/competition between plastic flow and void evolution.

q2 — parameter · Scalar · required

Void evolution rate

q3 — parameter · Scalar · required

Pore pressure